In an airborne or space context, passive locating of transmitters can be performed by various schemes such as for example, by measurements of angle of arrival (or AOA), of phase evolution over a large base (or LBI for “Long Base Interferometer” or LBPDE for “Long Base Phase Difference Evolution”), of arrival time differences (or TDOA for “Time Difference Of Arrival”) between at least two carriers, or else by Lobe Transit Time Difference (LTTD).
Angle of arrival measurements are customarily used for passive location of transmitters. They require that the receivers be equipped either with an amplitude goniometer, or with an interferometer. The main defect of location by angle of arrival measurement is its lack of precision when the time allocated to location is short.
If a large base interferometer is available, it is possible to use LBPDE measurements, however these measurements are prone to ambiguities. Moreover, the current techniques of location by phase evolution on a large base or by arrival time difference do not take into account the periodic character of the most frequently encountered radar waveforms. This results, for these waveforms, in sub-optimal performance as much in terms of location precision as in terms of computational load and of use of the bandwidth between the carriers.
A so-called Bancroft location scheme is known from the prior art, in particular through “An Algebraic Solution of the GPS Equations” by Stephen Bancroft (IEEE Transactions AES VOL. AES-21, NO. 7 January 1985). In this publication, an explicit (non-iterative) least squares estimation of the position is set forth in a similar GPS context. The scheme does not make any particular assumption about the nature of the signal. However, if one attempts to directly extend the scheme presented to the case of a periodic pulse train, a system of three second-degree equations is found, which is not in general explicitly soluble. Moreover, numerous invalid solutions must be eliminated if the system is solved numerically.
A problem with passive location of transmitters with the aid of the pulse arrival times (or TOA for “Time Of Arrival”) arises from the number of measurements to be processed. During the interception of a signal, a measurement of TOA is associated with each pulse received. The number of intercepted pulses, hence of pulse arrival time measurements, rapidly becomes very large since these pulses are transmitted at a very high rate. Moreover, with the existing solutions, computing a location on the basis of the TOAs involves estimating the arrival time of each pulse.
The complexity of the estimation problem will therefore grow rapidly with the number of pulses. For example, for an explicit algorithm based on the linear least squares scheme, the asymptotic complexity is given by O(I2M) with I the number of unknown parameters to be estimated and M the number of measurements. In the case of estimation with the arrival times we have M=P (number of receivers)×N (number of pulses) and I=3 (space dimensions)+N (number of unknown transmission dates, i.e. number of pulses) i.e. an asymptotic complexity of O(N3P) which is prohibitive in view of the number of pulses that might be received.
Concerning location based on pulse arrival time differences, since a difference between the measurements is computed, it is no longer necessary to estimate the dates of transmission of each pulse. However, the computation of this difference increases the variance of the measurements of TDOA with respect to those of TOA and causes correlations to appear between the measurements. The covariance matrix of the measurements of pulse arrival time differences is:
      Σ    TDOA    =            σ      TOA      2        ·          [                                    2                                1                                …                                1                                                1                                2                                …                                1                                                1                                1                                ⋱                                ⋮                                                1                                1                                …                                2                              ]      instead of:
      Σ    TOA    =            σ      TOA      2        ·          [                                    1                                0                                …                                0                                                0                                1                                …                                0                                                0                                0                                ⋱                                ⋮                                                0                                0                                …                                1                              ]      
The increase in the diagonal terms and the introduction of off-diagonal terms in the covariance matrix of the measurements leads to a slight degradation in location performance.
Moreover, the elimination of the “date of transmission” parameter corresponding to the pulse transmission start date removes the possibility of introducing a priori knowledge about this parameter. However, an a priori makes it possible to introduce additional information into the estimator thereby making it possible to improve the performance of final location.
Another problem with passive location by TOA or TDOA is related to the communications between the platforms. One or the other of the two previous schemes involves a communication between the platforms so as to compute the location results. The information dispatched from one platform to the other is the arrival times of the received pulses. Since the number of pulses received is considerable and the arrival times must be dispatched precisely (coded on a number of considerable bits), there is therefore a strong constraint on the bitrate of the data link. Moreover these dispatches penalize the discretion of the platforms.